scholarly journals Simplicity of partial skew group rings with applications to Leavitt path algebras and topological dynamics

2014 ◽  
Vol 420 ◽  
pp. 201-216 ◽  
Author(s):  
Daniel Gonçalves ◽  
Johan Öinert ◽  
Danilo Royer
Keyword(s):  
Topological Dynamics ◽  
Group Rings ◽  
Path Algebras ◽  
Skew Group Rings ◽  
Leavitt Path Algebras

scholarly journals Leavitt Path Algebras as Partial Skew Group Rings

2014 ◽  
Vol 42 (8) ◽  
pp. 3578-3592 ◽  
Author(s):  
Daniel Gonçalves ◽  
Danilo Royer
Keyword(s):  
Group Rings ◽  
Path Algebras ◽  
Skew Group Rings ◽  
Leavitt Path Algebras

scholarly journals SIMPLICITY AND CHAIN CONDITIONS FOR ULTRAGRAPH LEAVITT PATH ALGEBRAS VIA PARTIAL SKEW GROUP RING THEORY

2019 ◽  
Vol 109 (3) ◽  
pp. 299-319 ◽  
Author(s):  
DANIEL GONÇALVES ◽  
DANILO ROYER
Keyword(s):  
Group Ring ◽  
Ring Theory ◽  
Group Rings ◽  
Chain Conditions ◽  
Path Algebras ◽  
Skew Group Rings ◽  
Leavitt Path Algebras ◽  
Skew Group Ring

AbstractWe realize Leavitt ultragraph path algebras as partial skew group rings. Using this realization we characterize artinian ultragraph path algebras and give simplicity criteria for these algebras.

scholarly journals TRACES ON SEMIGROUP RINGS AND LEAVITT PATH ALGEBRAS

2015 ◽  
Vol 58 (1) ◽  
pp. 97-118 ◽  
Author(s):  
ZACHARY MESYAN ◽  
LIA VAŠ
Keyword(s):  
Commutative Rings ◽  
Inverse Semigroups ◽  
Linear Functions ◽  
Group Rings ◽  
Semigroup Rings ◽  
Matrix Rings ◽  
Path Algebras ◽  
Leavitt Path Algebras ◽  
The Many

AbstractThe trace on matrix rings, along with the augmentation map and Kaplansky trace on group rings, are some of the many examples of linear functions on algebras that vanish on all commutators. We generalize and unify these examples by studying traces on (contracted) semigroup rings over commutative rings. We show that every such ring admits a minimal trace (i.e., one that vanishes only on sums of commutators), classify all minimal traces on these rings, and give applications to various classes of semigroup rings and quotients thereof. We then study traces on Leavitt path algebras (which are quotients of contracted semigroup rings), where we describe all linear traces in terms of central maps on graph inverse semigroups and, under mild assumptions, those Leavitt path algebras that admit faithful traces.

scholarly journals On the representations of Leavitt path algebras

2011 ◽  
Vol 333 (1) ◽  
pp. 258-272 ◽  
Author(s):  
Daniel Gonçalves ◽  
Danilo Royer
Keyword(s):  
Path Algebras ◽  
Leavitt Path Algebras

scholarly journals FP-injective semirings, semigroup rings and Leavitt path algebras

2016 ◽  
Vol 45 (5) ◽  
pp. 1893-1906 ◽  
Author(s):  
Marianne Johnson ◽  
Tran Giang Nam
Keyword(s):  
Semigroup Rings ◽  
Path Algebras ◽  
Leavitt Path Algebras
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